1,630 research outputs found
A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics
This paper studies homogenization of stochastic differential systems. The
standard example of this phenomenon is the small mass limit of Hamiltonian
systems. We consider this case first from the heuristic point of view,
stressing the role of detailed balance and presenting the heuristics based on a
multiscale expansion. This is used to propose a physical interpretation of
recent results by the authors, as well as to motivate a new theorem proven
here. Its main content is a sufficient condition, expressed in terms of
solvability of an associated partial differential equation ("the cell
problem"), under which the homogenization limit of an SDE is calculated
explicitly. The general theorem is applied to a class of systems, satisfying a
generalized detailed balance condition with a position-dependent temperature.Comment: 32 page
Hadamard States and Adiabatic Vacua
Reversing a slight detrimental effect of the mailer related to TeXabilityComment: 10pages, LaTeX (RevTeX-preprint style
On Unitary Evolution of a Massless Scalar Field In A Schwarzschild Background: Hawking Radiation and the Information Paradox
We develop a Hamiltonian formalism which can be used to discuss the physics
of a massless scalar field in a gravitational background of a Schwarzschild
black hole. Using this formalism we show that the time evolution of the system
is unitary and yet all known results such as the existence of Hawking radiation
can be readily understood. We then point out that the Hamiltonian formalism
leads to interesting observations about black hole entropy and the information
paradox.Comment: 45 pages, revte
Dark Energy as a Relic of the Vacuum-Energy Cancellation?
We analyze the dynamical implications of an exponential Lagrangian density
for the gravitational field, as referred to an isotropic FRW Universe. Then, we
discuss the features of the generalized deSitter phase, predicted by the new
Friedmann equation. The existence of a consistent deSitter solution arises only
if the ratio between the vacuum-energy density and that associated with the
fundamental length of the theory acquires a tantalizing negative character.
This choice allows us to explain the present universe dark energy as a relic of
the vacuum-energy cancellation due to the cosmological constant intrinsically
contained in our scheme. The corresponding scalar-tensor description of the
model is addressed too, and the behavior of the scalar field is analyzed for
both negative and positive values of the cosmological term. In the first case,
the Friedmann equation is studied both in vacuum and in presence of external
matter, while, in the second case, the quantum regime is approached in the
framework of ''repulsive'' properties of the gravitational interaction, as
described in recent issues in Loop Quantum Cosmology. In particular, in the
vacuum case, we find a pure non-Einsteinian effect, according to which a
negative cosmological constant provides an accelerating deSitter dynamics, in
the region where the series expansion of the exponential term does not hold.Comment: 24 pages, 2 figures, to appear on IJMP
Conformal Invariance of Black Hole Temperature
It is shown that the surface gravity and temperature of a stationary black
hole are invariant under conformal transformations of the metric that are the
identity at infinity. More precisely, we find a conformal invariant definition
of the surface gravity of a conformal Killing horizon that agrees with the
usual definition(s) for a true Killing horizon and is proportional to the
temperature as defined by Hawking radiation. This result is reconciled with the
intimate relation between the trace anomaly and the Hawking effect, despite the
{\it non}invariance of the trace anomaly under conformal transformations.Comment: 8 pages, plain LaTeX, NSF-ITP-93-9
Feynman Propagator for a Free Scalar Field on a Causal Set
The Feynman propagator for a free bosonic scalar field on the discrete
spacetime of a causal set is presented. The formalism includes scalar field
operators and a vacuum state which define a scalar quantum field theory on a
causal set. This work can be viewed as a novel regularisation of quantum field
theory based on a Lorentz invariant discretisation of spacetime.Comment: 4 pages, 2 plots. Minor updates to match published versio
The exponential law: Monopole detectors, Bogoliubov transformations, and the thermal nature of the Euclidean vacuum in RP^3 de Sitter spacetime
We consider scalar field theory on the RP^3 de Sitter spacetime (RP3dS),
which is locally isometric to de Sitter space (dS) but has spatial topology
RP^3. We compare the Euclidean vacua on RP3dS and dS in terms of three
quantities that are relevant for an inertial observer: (i) the stress-energy
tensor; (ii) the response of an inertial monopole particle detector; (iii) the
expansion of the Euclidean vacuum in terms of many-particle states associated
with static coordinates centered at an inertial world line. In all these
quantities, the differences between RP3dS and dS turn out to fall off
exponentially at early and late proper times along the inertial trajectory. In
particular, (ii) and (iii) yield at early and late proper times in RP3dS the
usual thermal result in the de Sitter Hawking temperature. This conforms to
what one might call an exponential law: in expanding locally de Sitter
spacetimes, differences due to global topology should fall off exponentially in
the proper time.Comment: 22 pages, REVTex v3.1 with amsfonts and epsf, includes 2 eps figures.
(v2: Minor typos corrected, references updated.
Considerations on the Unruh Effect: Causality and Regularization
This article is motivated by the observation, that calculations of the Unruh
effect based on idealized particle detectors are usually made in a way that
involves integrations along the {\em entire} detector trajectory up to the
infinitely remote {\em future}. We derive an expression which allows
time-dependence of the detector response in the case of a non-stationary
trajectory and conforms more explicitely to the principle of causality, namely
that the response at a given instant of time depends only on the detectors {\em
past} movements. On trying to reproduce the thermal Unruh spectrum we are led
to an unphysical result, which we trace down to the use of the standard
regularization t\to t-i\eps of the correlation function. By consistently
employing a rigid detector of finite extension, we are led to a different
regularization which works fine with our causal response function.Comment: 19 pages, 2 figures, v2: some minor change
The effect of geometry on charge confinement in three dimensions
We show that, in contrast to the flat case, the Maxwell theory is not
confining in the background of the three dimensional BTZ black-hole (covering
space). We also study the effect of the curvature on screening behavior of
Maxwell-Chern-Simons model in this space-time.Comment: 8 pages. To be published in Europhysics Letter
Renormalization Ambiguities and Conformal Anomaly in Metric-Scalar Backgrounds
We analyze the problem of the existing ambiguities in the conformal anomaly
in theories with external scalar field in curved backgrounds. In particular, we
consider the anomaly of self-interacting massive scalar field theory and of
Yukawa model in the massless conformal limit. In all cases the ambiguities are
related to finite renormalizations of a local non-minimal terms in the
effective action. We point out the generic nature of this phenomenon and
provide a general method to identify the theories where such an ambiguity can
arise.Comment: RevTeX, 10 pages, no figures. Small comment and two references added.
Accepted for publication in Physical Review
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